Journal of Monetary Economics 49 (2002) 989–1015
Monetary policy rules in the open economy:
effects on welfare and business cycles$
Robert Kollmanna,b,*
a Department of Economics, University of Bonn, 24-42 Adenauerallee, D-53113 Bonn, Germany
b Centre for Economic Policy Research, UK
Received 16 November 2001; received in revised form 4 March 2002; accepted 5 March 2002
Abstract
This paper computes welfare maximizing Taylor-style interest rate rules, in a business cycle
model of a small open economy. The model assumes staggered price setting and shocks to
domestic productivity, to the world interest rate, to world inflation, and to the uncovered
interest rate parity condition. Optimized policy rules have a pronounced anti-inflation stance
and entail significant nominal and real exchange rate volatility. The country responds to an
increase in external volatility by holding more foreign assets. The policy rule affects the
variance and the mean of consumption. The effect on the mean matters significantly for
welfare. r 2002 Elsevier Science B.V. All rights reserved.
JEL classification: E4; F3; F4
Keywords: Open economy; Interest rate rules; Business cycles
$This paper was prepared for the November 2001 Carnegie-Rochester Conference on Public Policy. I
thank Ben McCallum for encouragement and advice, and Andy Levin and other conference participants
for useful comments. I am grateful to Jinill Kim, Stephanie Schmitt-Groh!e, and Chris Sims, for
discussions/advice on computational issues. Thanks for helpful discussions are also due to Gianluca
Benigno, Pierpaolo Benigno, Paul Bergin, Luca Dedola, Chris Erceg, Mark Gertler, Soyoung Kim,
Sylvain Leduc, Tommaso Monacelli, Ed Nelson, Paolo Pesenti, Frank Smets, Pedro Teles, Harald Uhlig,
Mart!ın Uribe, Michael Woodford, and Raf Wouters, as well as to seminar participants at the North
American Winter Meetings of the Econometric Society.
*Corresponding author. Tel.: +49-228-734073; fax: +49-228-739100.
E-mail address: kollmann@wiwi.uni-bonn.de (R. Kollmann).
0304-3932/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 3 0 4 - 3 9 3 2 ( 0 2 ) 0 0 1 3 2 - 0

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R. Kollmann / Journal of Monetary Economics 49 (2002) 989–1015
1. Introduction
The effect of the monetary policy regime on welfare and business cycles is a key
question in economics. This paper examines that question using a micro-based
quantitative (calibrated) business cycle model of a small open economy in which
monetary policy affects real activity because of staggered price setting.
Much effort has recently been devoted to develop dynamic general equilibrium
models of open economies with monopolistic competition and sluggish prices (or
wages)—see Lane (2001) for a survey of that work, often referred to as ‘‘New Open
Economy Macroeconomics’’ (NOEM). An important strand of the NOEM literature
uses highly stylized models (for which analytical results can be worked out) to
determine welfare under alternative exchange rate regimes and to derive optimal
monetary policy rules. The simplifying assumptions generally made in these models
include, in particular: full international risk sharing, a stripped-down structure of
shocks (mostly just one type of shock—productivity shocks), and the absence of
physical capital.1 Another strand of the literature develops quantitative business
cycle models that can be used to study the key features of international
macroeconomic data.2
The models studied in the first strand seem too stylized for empirical analysis,
whereas computing welfare (and welfare maximizing policy rules) in quantitative
business cycle models has, until now, not been practically feasible, given available
numerical techniques. The paper here bridges these two approaches by determining
welfare maximizing Taylor (1993a)-style interest rate rules, using a quantitative
business cycle model. This is made possible by recent advances in solving dynamic
models (Sims, 2000).
The model here extends the sticky-prices open economy model that Kollmann
(2001a) calibrated to data for Japan, Germany and the U.K. It assumes
imperfect international risk sharing due to incomplete international financial
markets (transactions restricted to trade in bonds) and physical capital (like
standard business cycle models). In the model, there are shocks to domestic
productivity, to the world interest rate, to world inflation, and to the uncovered
interest parity condition (‘‘UIP shocks’’). Monetary policy is described by a rule
according to which the nominal interest rate is set as a function of the inflation rate
and of GDP.
1 See, for example, Bacchetta and van Wincoop (2000), Benigno (2000, 2001), Clarida et al. (2001),
Corsetti and Pesenti (2001), Devereux and Engel (2000), Gal!ı and Monacelli (2000), Obstfeld and Rogoff
(2000), Parrado and Velasco (2001), and Sutherland (2001).
2 See, for example, Batini et al. (2001), Benigno (1999), Bergin (2001), Betts and Devereux (2001), Chari
et al. (2000), Collard and Dellas (2002), Dedola and Leduc (2001), Duarte and Stockman (2001), Erceg
and Levin (2001), Faia (2001), Ghironi and Rebucci (2001), Hairault et al. (2001), Kollmann (2001a, b;
2002), McCallum and Nelson (1999, 2000), Monacelli (1999), Schmitt-Groh!e and Uribe (2001a), and
Smets and Wouters (2000, 2001).

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991
Imperfect risk sharing is more realistic than the complete risk sharing assumed in
previous welfare analyses.3 In the bonds-only structure here, macroeconomic
variability affects the mean net foreign asset position—which has significant
consequences for welfare.4 That effect is not present in models with complete risk
sharing.
UIP shocks are assumed here because of the well-documented strong and
persistent departures from UIP during the post-Bretton Woods (post-BW) era (e.g.,
Lewis, 1995). Also, econometric attempts to explain short-run exchange rate
movements from changes in monetary policy (and other macro fundamentals) have
failed (e.g., Rogoff, 2000). Structural models driven only by ‘‘traditional’’
fundamentals generate predicted exchange rate variability that is much smaller than
that seen in post-BW data; thus, such models are not well suited to analyzing a
floating-rate regime. The model here—with UIP shocks—generates more realistic
exchange rate volatility; the predicted standard deviation of the Hodrick–Prescott
(HP) filtered nominal exchange rate is 7.1% (in a version of the model without UIP
shocks, the corresponding standard deviation is 3.4%); the standard deviations of
HP filtered quarterly exchange rates of Japan, Germany and the U.K. vis-"a-vis the
U.S. were about 9% during the post-BW era. (In the NOEM literature, only
McCallum and Nelson (1999) and Batini and Nelson (2000) compare alternative
policy rules using models with UIP shocks, but these authors do not compute
welfare.)
The present model is solved using Sims’ (2000) new method that is based on a
quadratic approximation of the equilibrium conditions. In contrast to the solution
methods based on linear approximations that are widely used in macroeconomics,
the Sims approach allows to compute the (second-order accurate) effect of the policy
rule on expected values of macroeconomic variables—an effect that is crucial for
welfare in the model here. Compared with other non-linear solution methods (see
Judd, 1998), the Sims method has two key advantages—the ease with which it can be
applied to models with a large number of state variables and its high computational
speed. These features allow to numerically determine the coefficients of the monetary
policy rule that maximize welfare.5
The optimized rule entails rather strict (but not perfect) targeting of the growth
rate of the domestic producer price index (PPI): the implied standard deviation of
PPI inflation is low (0.08%). It yields a welfare level that is close to that of the
economy under flexible prices. The domestic interest rate falls in response to positive
shocks to domestic productivity; it shows little response to UIP shocks and to shocks
to the world interest rate and to world inflation. The rule implies significant nominal
3 Models with complete risk sharing typically generate cross-country consumption correlations that are
much too high, when compared to the data; a bonds-only structure can generate correlations that are
markedly lower (and, thus, closer to the data); e.g., Backus et al. (1995) and Kollmann (1995, 1996).
4 In the model, stationarity of the net asset position is ensured by assuming a debt-elastic interest rate
premium on international bonds.
5 Smets and Wouters (2000, 2001) also discuss welfare in a calibrated open economy model with
incomplete financial markets (but without capital or UIP shocks). These authors do not compute the effect
of the policy rule on expected values of macrovariables.

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R. Kollmann / Journal of Monetary Economics 49 (2002) 989–1015
and real exchange rate volatility. Permitting a direct response of the interest rate rule
to the nominal exchange rate yields only a minuscule welfare gain. Under the
optimized rule, productivity shocks are the main source of fluctuations in output and
consumption, while UIP shocks are the dominant source of exchange rate
fluctuations. UIP shocks have a positive effect on welfare i.a. because they lead
the country to hold a larger stock of foreign bonds. Hence, with UIP shocks, the
country is wealthier (on average), and it enjoys higher mean consumption.
Prior research shows that when price stickiness (in producer currency) is the only
economic distortion (so that the flex-prices equilibrium of the economy is efficient),
and exchange rate changes are fully and immediately passed through into import
prices (ensuring that the law of one price (LOP) holds), then welfare maximizing
monetary policy requires perfect stabilization of the domestic PPI (e.g., Aoki, 2001;
Devereux and Engel, 2000; Gal!ı and Monacelli, 2000). That policy replicates the flex-
prices equilibrium and entails a floating exchange rate. Full PPI stabilization is not
optimal when (as in the model here) the flex-prices equilibrium is not efficient (here:
i.a. monopolistic distortions) or when exchange rate pass through is limited. It thus
seems worth noting that the optimized policy rule, in the economy discussed here,
does entail rather strict (but not perfect) PPI inflation targeting, and that it yields a
welfare level close to that in the flex-prices economy. The results suggest that (near)
PPI inflation stabilization is also desirable under the more realistic assumption that
exchange rate pass through is limited, as a result of pricing-to-market (PTM) (the
data clearly reject full pass through and the LOP; see, e.g., Knetter, 1993; Campa
and Goldberg, 2001).
In the model here, pegging the exchange rate reduces welfare. Under a peg,
external shocks require strong and immediate adjustment of the domestic interest
rate—these shocks thus have a more destabilizing effect on consumption (than under
the optimized rule). In addition, a peg reduces mean consumption, since the
increased volatility of goods demand under a peg induces firms to set higher price-
marginal cost markups. Under the plausible assumption that pegging the exchange
rate reduces the variance of UIP shocks (UIP shocks were smaller under the BW
system than in the post-BW era), the country holds a smaller stock of foreign bonds
under a peg—which also lowers welfare.
The model captures the fact that nominal and real exchange rate volatility among
the major currency blocs has risen sharply after the end of the BW system, whereas
output volatility has shown little change (e.g., Baxter and Stockman, 1989).
Section 2 of this paper presents the model and discusses the solution method,
Section 3 presents the results and Section 4 concludes.
2. The model
A small open economy with a representative household, firms, and a central bank
is considered (the structure of preferences and technologies follows Kollmann,
2001a). The economy produces a single non-tradable final good and a continuum of
tradable intermediate goods indexed by sA½0; 1Š: It imports a continuum of foreign

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R. Kollmann / Journal of Monetary Economics 49 (2002) 989–1015
993
intermediate goods, also indexed by sA½0; 1Š: Domestic and foreign intermediate
goods are used by perfectly competitive firms to produce the final good which is
consumed and used for investment. There is monopolistic competition in
intermediate goods markets—each intermediate good is produced or imported by
a single firm. Intermediate goods producers use domestic capital and labor as
inputs—capital and labor are immobile internationally. The household owns all
domestic producers and the capital stock, which it rents to producers. It also supplies
labor. The markets for rental capital and for labor are competitive.
2.1. Final good production
The final good is produced using the aggregate technology
Zt ¼ fðadÞ1=WðQdÞðWÀ1Þ=W þ ðamÞ1=WðQmÞðWÀ1Þ=WgW=ðWÀ1Þ;
ð1Þ
t
t
with ad; am > 0; ad þ am ¼ 1; W > 0: Zt is final good output at date t; Qd; Qm are
t
t
quantity indices of domestic and imported intermediate goods, respectively: Qi ¼
t
R
f 1 qi ðsÞðnÀ1Þ=n dsgn=ðnÀ1Þ with n > 1 for i=d,m, where qdðsÞ and qmðsÞ are quantities of
0
t
t
t
the domestic and imported type s intermediate goods. Let pdðsÞ and pmðsÞ be the
t
t
prices of these goods in domestic currency. Cost minimization in final good
production implies
qi ðsÞ ¼ ðpi ðsÞ=Pi ÞÀnQi ;
Qi ¼ aiðPi =P
t
t
t
t
t
t
tÞÀWZt
for i ¼ d; m;
ð2Þ
with
Z 1
1=ð1ÀnÞ
Pi ¼
pi ðsÞ1Àn ds
;
P
Þ1ÀW þ amðPmÞ1ÀWg1=ð1ÀWÞ:
ð3Þ
t
t
t ¼ fadðPd
t
t
0
Pd½PmŠ is a price index for domestic [imported] intermediate goods that are sold in
t
t
the domestic market. Perfect competition in the final good market implies that the
good’s price is Pt (its marginal cost is fadðPdÞ1ÀW þ amðPmÞ1ÀWg1=ð1ÀWÞ).
t
t
2.2. Intermediate goods firms
The technology of the firm that produces domestic intermediate good s is
ytðsÞ ¼ ytKtðsÞcLtðsÞ1Àc;
0oco1:
ð4Þ
ytðsÞ is the firm’s output at date t; yt is an exogenous productivity parameter that is
identical for all domestic intermediate goods producers; KtðsÞ and LtðsÞ are the
amounts of capital and labor used by the firm.
Let Rt and Wt be the rental rate of capital and the wage rate. Cost minimization
implies: LtðsÞ=KtðsÞ ¼ cÀ1ð1 À cÞRt=Wt: The firm’s marginal cost is MCt ¼
ð1=ytÞRctW 1Àc
t
cÀcð1 À cÞcÀ1:
The firm’s good is sold in the domestic market and exported: yt ¼ qdðsÞ þ qxðsÞ;
t
t
where qdðsÞ [qxðsÞ] is domestic [export] demand. The export demand function is
t
t

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R. Kollmann / Journal of Monetary Economics 49 (2002) 989–1015
assumed to resemble the domestic demand function (2):
qxðsÞ ¼ ðpxðsÞ=PxÞÀnQx;
with Qx ¼ ðPx=PnÞÀZ; Z > 0;
ð5Þ
t
t
t
t
t
t
t
where pxðsÞ is the firm’s export price in foreign currency, while
t
Z 1
n=ðnÀ1Þ
Z 1
1=ð1ÀnÞ
Qx ¼
qxðsÞðnÀ1Þ=n ds
;
Px ¼
pxðsÞ1Àn ds
ð6Þ
t
t
t
t
0
0
are a quantity index and a price index for the country’s exports. Pn is the world price
t
level and also represents the purchase price of foreign intermediate goods paid by
domestic importers; Pn is exogenous.
t
The profits of a domestic intermediate good producer, pdx; and of an intermediate
t
good importer, pm; are:
t
pdxðpdðsÞ; pxðsÞÞ
t
t
t
¼ ðpdðsÞ À MC
ðsÞ=PdÞÀnQd þ ðe
ðsÞ À MC
ðsÞ=PxÞÀnQx;
t
tÞðpd
t
t
t
tpx
t
tÞðpx
t
t
t
pmðpmðsÞÞ ¼ ðpmðsÞ À e
ÞðpmðsÞ=PmÞÀnQm;
ð7Þ
t
t
t
tPn
t
t
t
t
where et is the nominal exchange rate, expressed as the domestic currency price of
foreign currency.
Motivated by the empirical failure of the LOP, and in particular by widespread
PTM behavior (e.g., Knetter, 1993), it is assumed that intermediate goods producers
can price discriminate between the domestic market and the export market
(pdðsÞae
ðsÞ is possible), and that they set prices in the currencies of their
t
tpx
t
customers.
There is staggered price setting, "a la Calvo (1983): intermediate goods firms cannot
change prices, in buyer currency, unless they receive a random ‘‘price-change signal’’.
The probability of receiving this signal in any particular period is 1 À d; a constant.
Thus, the mean price-change-interval is 1=ð1 À dÞ: Following Yun (1996) and Erceg
et al. (2000) it is assumed that when a firm does not receive a ‘‘price-change signal’’,
its price is automatically increased at the steady state growth factor of the price level
(in the buyer’s country). (Throughout this paper, the term ‘‘steady state’’ refers to
the deterministic steady state.) Firms are assumed to meet all demand at posted
prices.
Consider an intermediate good producer that, at time t, sets a new price in the
domestic market, pd : If no ‘‘price-change signal’’ is received between t and t þ t; the
t;t
price is pd Pt at t þ t; where P is the steady-state growth factor of the domestic price
t;t
level. The firm sets
X
t¼N
pd ¼ Arg Max
dtE
ðPPt; px ðsÞÞ=P
t;t
tfrt;tþtpdx
tþt
tþt
tþtg;
P
t¼0
where rt;tþt is a pricing kernel (for valuing date t þ t payoffs) that equals the
household’s marginal rate of substitution between consumption at t and at t þ t (see
discussion below). Let Xi
¼ r
ðP
ðPi
Þn; for i=d,x. The solution
t;tþt
t;tþt
t=PtþtÞ Qitþt
tþt

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R. Kollmann / Journal of Monetary Economics 49 (2002) 989–1015
995
of the maximization problem regarding pd is
t;t
X
n
on
o
t¼N
Xt¼N
pd ¼ ðn=ðn À 1ÞÞ
ðdPÀnÞtE
MC
ðdP1ÀnÞtE
:
t;t
tXd
tþt
tXd
t¼0
t;tþt
t¼0
t;tþt
ð8Þ
Analogously, an intermediate good producer that gets to choose a new export
price at date t sets that price at
(
) (
)
X
t¼N
 X
t¼N
px ¼ ðn=ðn À 1ÞÞ
ðdðPnÞÀnÞtE
MC
ðdðPnÞ1ÀnÞtE
e
;
t;t
tXx
t;tþt
tþt
tXx
t;tþt tþt
t¼0
t¼0
ð9Þ
where Pn is the steady-state growth factor of the world price level.
Firms that import foreign intermediate goods are owned by risk-neutral foreigners
who discount future payoffs using the world nominal interest rate.6 An importer that
gets to set a new price selects
X
t¼N
pm ¼ Arg Max
dtE
ðPPtÞ=e
t;t
tfRt;tþtpm
tþt
tþtg
P
t¼0 Q
with R
k¼tÀ1
t;t ¼ 1 and Rt;tþt ¼
ð1 þ in ÞÀ1
for t > 1; where in is the world interest
k¼1
tþk
t
rate between t and t þ 1: The solution of this decision problem is
nX
on
o
t¼N
Xt¼N
pm ¼ ðn=ðn À 1ÞÞ
ðdPÀnÞtE
Pn
ðdP1ÀnÞtE
=e
t;t
tXm
tXm
tþt
t¼0
t;tþt
tþt
t¼0
t;tþt
ð10Þ
with Xm
¼ R
ðPm Þn:
t;tþt
t;tþtQm
tþt
tþt
The price indices Pd; Pm; Px (see (3) and (6)) evolve according to
t
t
t
ðPi Þ1Àn ¼ dðPi
PÞ1Àn þ ð1 À dÞðpi Þ1Àn;
i¼ d; m;
t
tÀ1
t;t
ðPxÞ1Àn ¼ dðPx PnÞ1Àn þ ð1 À dÞðpx Þ1Àn:
ð11Þ
t
tÀ1
t;t
2.3. The representative household
Household preferences are described by
X
t¼N
E0
btU ðCt; LtÞ:
ð12Þ
t¼0
Et denotes the mathematical expectation conditional upon complete information
pertaining to period t and earlier. Ct and Lt are period t consumption and labor
effort. 0obo1 is the subjective discount factor. U is a utility function given by
U ðCt; LtÞ ¼ lnðCtÞ À Lt:
ð13Þ
6 It might seem preferable to assume that importers discount future payoffs at the intertemporal
marginal rate of substitution of foreign households. This would require modeling the consumption
behavior of those households—which is beyond the scope of the small open economy model here.

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R. Kollmann / Journal of Monetary Economics 49 (2002) 989–1015
As indicated earlier, the household owns all domestic producers and accumulates
physical capital. The law of motion of the capital stock is
Ktþ1 þ fðKtþ1; KtÞ ¼ Ktð1 À dÞ þ It;
ð14Þ
where It is the gross investment, 0odo1 is the depreciation rate of capital, and f is
an adjustment cost function: fðKtþ1; KtÞ ¼ 1FfK
2
tþ1 À Ktg2=Kt; F > 0:
The household also holds nominal one-period domestic and foreign currency
bonds. Its period t budget constraint is
Atþ1 þ etBtþ1 þ PtðCt þ ItÞ ¼ Atð1 þ itÀ1Þ þ etBtð1 þ if Þ
tÀ1
Z 1
þ RtKt þ
pdxðsÞ ds þ W
t
tLt:
ð15Þ
0
At and Bt are net stocks of domestic and foreign currency bonds that mature in
period t, while itÀ1 and if
are the interest rates on these bonds.
tÀ1
The household chooses a strategy fAtþ1; Btþ1; Ktþ1; Ct; Ltgt¼N to maximize its
t¼0
expected lifetime utility (12), subject to constraints (14) and (15) and to initial values
A0; B0; K0: Ruling out Ponzi schemes, the following equations are first-order
conditions of this decision problem:
1 ¼ ð1 þ itÞEtfr
ðP
t;tþ1
t=Ptþ1Þg;
ð16Þ
1 ¼ ð1 þ if ÞE
ðP
t
tfrt;tþ1
t=Ptþ1Þðetþ1=etÞg;
ð17Þ
1 ¼ Etfr
ðR
Þ
Þg
t;tþ
=ð
;
ð
1
tþ1=Ptþ1 þ 1 À d À f2;tþ1
1 þ f1;t
18Þ
Wt=Pt ¼ Ct;
ð19Þ
where r
¼
¼
¼
t;tþ1
bCt=Ctþ1; f1;t
qfðKtþ1; KtÞ=qKtþ1; f2;tþ1
qfðKtþ2; Ktþ1Þ=qKtþ1:
Eqs. (16)–(18) are Euler conditions, and (19) says that the household equates its
marginal rate of substitution between consumption and leisure to the real wage rate.
2.4. Uncovered interest parity
Up to a (log-)linear approximation, (16) and (17) imply uncovered interest parity
(UIP): Et lnðetþ1=etÞDit À if : Given the well-documented strong and persistent
t
empirical departures from UIP during the post-BW era (e.g., Lewis, 1995), variants
of the model are explored in which the Euler condition for foreign currency bonds
(17) is disturbed by a stationary exogenous stochastic random variable, jt (‘‘UIP
shock’’, henceforth) whose unconditional mean is unity (Ej ¼
t
1):
1 ¼ j ð
Þ
ðP
t 1 þ if E
t
tfrt;tþ1
t=Ptþ1Þðetþ1=etÞg:
ð20Þ
(Up to a (log-)linear approximation, (16) and (20) imply Et lnðetþ1=etÞDit À if À
t
ðj À
t
1Þ:) As discussed in the Appendix, jt can be interpreted as reflecting a bias in
the household’s date t forecast of the date t+1 exchange rate, etþ1: (Frankel and
Froot (1989), document biases in exchange rate forecasts; structural models with
UIP shocks have, i.e., been studied by Mark and Wu (1998) and Jeanne and Rose

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R. Kollmann / Journal of Monetary Economics 49 (2002) 989–1015
997
(2000), who interpret these shocks as ‘‘fads’’, and by McCallum and Nelson (1999,
2000), and Taylor (1993b), who refer to them as ‘‘risk premia’’.)
2.5. Market clearing conditions
Supply equals demand in intermediate goods markets because intermediate goods
firms meet all demand at posted prices. Market clearing for the final good, labor, and
rental capital requires:
Z 1
Z 1
Zt ¼ Ct þ It;
Lt ¼
LtðsÞ ds;
Kt ¼
KtðsÞ ds:
ð21Þ
0
0
Zt; Lt and Kt are the supplies of the final good, of labor, and of rental capital,
R
R
respectively, while
1 L
1 K
0
tðsÞ ds and
0
tðsÞ ds represent total demand for labor and
capital (by intermediate goods producers).
It is assumed that foreigners do not hold bonds denominated in the currency of the
small open economy. Thus, market clearing for bonds of this type requires
At ¼ 0:
ð22Þ
if ; the interest rate at which the household can borrow/lend foreign currency funds
t
equals the exogenous world interest rate, in; plus a ‘‘spread’’ that is a decreasing
t
function of the country’s net foreign asset position:
ð1 þ if Þ=Pn ¼ ð1 þ inÞ=Pn À lðB
Þ=w;
l > 0;
ð23Þ
t
t
tþ1=Pn
t
where w is the steady-state value of exports, expressed in units of foreign output
(PxQx=Pn). l captures the degree of capital mobility—a lower l represents higher
t
t
t
capital mobility. Under perfect mobility (l ¼ 0), the country would face an infinite
supply of/demand for foreign funds when if ain: The simulations assume that
t
t
financial capital is not perfectly mobile (owing to transaction costs or other frictions):
l > 0: This ensures the existence of stationary equilibrium, which allows to solve the
model using the Sims (2000) method. (When l ¼ 0; the model is a version of the
permanent income theory of consumption, and net assets and consumption are non-
stationary. Schedules similar to (23) have also been assumed by Senhadji (1997) and
Schmitt-Groh!e and Uribe (2001a).)
2.6. Exogenous variables
Productivity, world inflation, the world interest rate, and the UIP shock follow
these processes:
yt ¼ ð1 À ryÞ þ ryytÀ1 þ ey;
0pryo1;
ð24Þ
t
Pn ¼ ð1 À rnÞPn þ rnPn
þ Pnen;
ð25Þ
t
tÀ1
t
where Pn ¼ Pn=Pn ;
0prno1;
t
t
tÀ1
in ¼ ð1 À riÞin þ riin
þ Pnei;
0prio1;
ð26Þ
t
tÀ1
t
j ¼ ð
þ
t
1 À rjÞ þ rjjtÀ1
ej
t ;
0prjo1;
ð27Þ

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998
R. Kollmann / Journal of Monetary Economics 49 (2002) 989–1015
where ey; en; ei ; and ej
t
t
t
t are independent white noises with standard deviations sy; sn;
si; and sj; respectively.
2.7. The monetary policy rule
Much recent research on monetary policy regimes has focused on rules that
stipulate a response of the interest rate to inflation and to real GDP (e.g., Taylor,
1993a, 1999). The baseline rule considered here is
it ¼ i þ Gp b
Pd þ G
t
y b
Yt;
ð28Þ
with b
Pd ¼ ðPd À PÞ=P; b
Y
¼ Pd=Pd
is the growth factor
t
t
t ¼ ðYt À Y Þ=Y ; where Pd
t
t
tÀ1
of the price index of domestic intermediate goods that are sold in the domestic
market—(gross) domestic PPI inflation. Yt is real GDP (measurement of GDP: see
Appendix). i and Y are the steady-state nominal interest rate and steady-state GDP,
respectively. Throughout the paper, variables without time subscripts denote steady-
state values, and #xt ¼ ðxt À xÞ=x is the relative deviation of a variable xt from its
steady-state value, x: Gp and Gy in (28) are parameters.
The central bank irrevocably commits to setting Gp and Gy at the values that
maximize the unconditional expected value of household utility, EðU ðCt; LtÞÞ: Note
that a fully optimal feedback rule would stipulate a response of the interest rate to all
current and lagged state variables (e.g., Clarida et al., 1999; Rotemberg and
Woodford, 1997). I focus on a ‘‘simple’’ rule such as (28) because: (i) simple rules
appear to capture quite well actual central bank behavior (e.g., Taylor, 1993a, 1999);
(ii) the use of a simple rule facilitates commitment as the public can easily monitor
whether the central bank sticks to such a rule; (iii) computationally, it does not seem
feasible to determine the fully optimal rule for the complex model considered here.7
2.8. Solution method, welfare measures
The model is solved using Sims’ (2000) second-order accurate method (see
Appendix), and EðU ðCt; LtÞÞ is maximized numerically with respect to the policy
parameters Gp and Gy (attention is restricted to parameter values for which a unique
stationary equilibrium exists).
A second-order Taylor expansion of the utility function around the steady state
gives EðU ðCt; LtÞÞDUðC; LÞ þ Eð b
CtÞ À LEð b
LtÞ À Varð b
CtÞ; where Varð b
CtÞ is the
variance of b
Ct: (For the parameter values used below, L=0.74.)
In what follows, welfare is expressed as the permanent relative change in
consumption (compared to the steady state), z; that yields expected utility
EðU ðCt; LtÞÞ:
U ðð1 þ zÞC; LÞ ¼ U ðC; LÞ þ Eð b
CtÞ À LEð b
LtÞ À Varð b
CtÞ:
z
can
be
7 The optimal rule can, in principle, be found by selecting the path of the interest rate (and of the other
endogenous variables) that maximizes welfare subject to the equilibrium conditions of the economy (e.g.,
Clarida et al., 1999). For the model here, this ‘‘Ramsey problem’’ is not a concave programming problem
and hence is intractable. Solving the system of equations obtained by setting to zero the derivatives of the
Lagrangian associated with the Ramsey problem is not feasible using the Sims algorithm.

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Document Outline

• Monetary policy rules in the open economy: effects on welfare and business cycles
  • Introduction
  • The model
    • Final good production
    • Intermediate goods firms
    • The representative household
    • Uncovered interest parity
    • Market clearing conditions
    • Exogenous variables
    • The monetary policy rule
    • Solution method, welfare measures
    • Parameters (non-policy)
  • Results
    • Results for the baseline sticky-prices model (Table 1, cols. 1-5)
      • Combined effect of shocks (Table 1, Col. 1)
      • The sticky-prices economy subjected to each type of shock separately
      • Explaining the mean foreign asset position
    • Results for the flex-prices variant of the model (Table 1, cols. 6-10)
      • Impulse responses (Table 2)
    • Why is welfare so similar under sticky prices (with optimized rule) and under flexible prices?
    • Exchange rate peg
      • Effects of a peg that eliminates UIP shocks
    • Other variants of the sticky-prices model
      • Alternative assumptions about price adjustment
      • Alternative policy rules
    • Standard deviations: comparing data and model predictions
  • Conclusions
  • References

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